About

Georg Stadler is a Professor of Mathematics and Computer Science at the Courant Institute of New York University. His research encompasses a range of topics including sea ice strain rates, rheology parameter inference in mantle flow, and the optimization of coils for stellarators. His work has been published in notable journals such as the Journal of Computational Physics, Nature Geoscience, and Physics of Plasmas. Stadler is based at the Courant Institute in New York City, where he contributes to both research and teaching in his fields of expertise.

Research topics

• Computer Science
• Paleontology
• Oceanography
• Geology
• Computational physics
• Seismology
• Mathematics
• Geometry
• Mathematical analysis
• Physics
• Quantum mechanics

Selected publications

• Learning parameter-dependent shear viscosity from data, with application to sea and land ice

  Journal of Computational Physics · 2026-04-25

  articleOpen accessSenior author
  PublisherOA PDFDOI

• Physics-informed reservoir characterization from bulk and extreme pressure events with a differentiable simulator

  arXiv (Cornell University) · 2026-04-14

  preprintOpen access

  Accurate characterization of subsurface heterogeneity is challenging but essential for applications such as reservoir pressure management, geothermal energy extraction and CO$_2$, H$_2$, and wastewater injection operations. This challenge becomes especially acute in extreme pressure events, which are rarely observed but can strongly affect operational risk. Traditional history matching and inversion techniques rely on expensive full-physics simulations, making it infeasible to handle uncertainty and extreme events at scale. Purely data-driven models often struggle to maintain physics consistency when dealing with sparse observations, complex geology, and extreme events. To overcome these limitations, we introduce a physics-informed machine learning method that embeds a differentiable subsurface flow simulator directly into neural network training. The network infers heterogeneous permeability fields from limited pressure observations, while training minimizes both permeability and pressure losses through the simulator, enforcing physical consistency. Because the simulator is used only during training, inference remains fast once the model is learned. In an initial test, the proposed method reduces the pressure inference error by half compared with a purely data-driven approach. We then extend the test over eight distinct data scenarios, and in every case, our method produces significantly lower pressure inference errors than the purely data-driven model. We also evaluate our method on extreme events, which represent high-consequence data in the tail of the sample distribution. Similar to the bulk distribution, the physics-informed model maintains higher pressure inference accuracy in the extreme event regimes. Overall, the proposed method enables rapid, physics-consistent subsurface inversion for real-time reservoir characterization and risk-aware decision-making.

  PublisherDOI

• Numerical experiments for segmenting medical images using level sets

  2026-01-22

  articleOpen accessSenior author

  Image segmentation is the process by which objects are separated from background information. Structural segmentation from 2D and 3D images is an important step in the analysis of medical image data. In this work, we utilize level set algorithms and active contours without edges to segment two and three-dimensional image data. Besides synthetical data, we also use magnetic resonance images of the human brain provided by the Institute of Biomedical Research in Light and Images of the University of Coimbra (IBILI).

  PublisherOA PDFDOI

• Infinite-dimensional spherical-radial decomposition for probabilistic functions, with application to constrained optimal control and Gaussian process regression

  arXiv (Cornell University) · 2026-03-20

  preprintOpen accessSenior author

  The spherical-radial decomposition (SRD) is an efficient method for estimating probabilistic functions and their gradients defined over finite-dimensional elliptical distributions. In this work, we generalize the SRD to infinite stochastic dimensions by combining subspace SRD with standard Monte Carlo methods. The resulting method, which we call hybrid infinite-dimensional SRD (hiSRD) provides an unbiased, low-variance estimator for convex sets arising, for instance, in chance-constrained optimization. We provide a theoretical analysis of the variance of finite-dimensional SRD as the dimension increases, and show that the proposed hybrid method eliminates truncation-induced bias, reduces variance, and allows the computation of derivatives of probabilistic functions. We present comprehensive numerical studies for a risk-neutral stochastic PDE optimal control problem with joint chance state constraints, and for optimizing kernel parameters in Gaussian process regression under the constraint that the posterior process satisfies joint chance constraints.

  PublisherDOI

• <b>Book Review:</b> An Introduction to Stellarators

  SIAM Review · 2026-02-09

  article1st authorCorresponding
  PublisherDOI

• Physics-informed reservoir characterization from bulk and extreme pressure events with a differentiable simulator

  ArXiv.org · 2026-04-14

  articleOpen access

  Accurate characterization of subsurface heterogeneity is challenging but essential for applications such as reservoir pressure management, geothermal energy extraction and CO$_2$, H$_2$, and wastewater injection operations. This challenge becomes especially acute in extreme pressure events, which are rarely observed but can strongly affect operational risk. Traditional history matching and inversion techniques rely on expensive full-physics simulations, making it infeasible to handle uncertainty and extreme events at scale. Purely data-driven models often struggle to maintain physics consistency when dealing with sparse observations, complex geology, and extreme events. To overcome these limitations, we introduce a physics-informed machine learning method that embeds a differentiable subsurface flow simulator directly into neural network training. The network infers heterogeneous permeability fields from limited pressure observations, while training minimizes both permeability and pressure losses through the simulator, enforcing physical consistency. Because the simulator is used only during training, inference remains fast once the model is learned. In an initial test, the proposed method reduces the pressure inference error by half compared with a purely data-driven approach. We then extend the test over eight distinct data scenarios, and in every case, our method produces significantly lower pressure inference errors than the purely data-driven model. We also evaluate our method on extreme events, which represent high-consequence data in the tail of the sample distribution. Similar to the bulk distribution, the physics-informed model maintains higher pressure inference accuracy in the extreme event regimes. Overall, the proposed method enables rapid, physics-consistent subsurface inversion for real-time reservoir characterization and risk-aware decision-making.

  PublisherOA PDF

• Optimal Control under Uncertainty with Joint Chance State Constraints: Almost-Everywhere Bounds, Variance Reduction, and Application to (Bi)linear Elliptic PDEs

  SIAM/ASA Journal on Uncertainty Quantification · 2025-08-06 · 3 citations

  article
  PublisherDOI

• A note on generating Voronoi cells with a given size distribution

  ArXiv.org · 2025-08-08

  preprintOpen access1st authorCorresponding

  This note describes a simple method to draw random points such that the cells of the corresponding Voronoi tesselation (approximately) satisfy a desired size distribution, for instance, follow a power law. The method is illustrated and numerically verified in two dimensions, and we also provide a simple implementation.

  PublisherOA PDFDOI

• Non-Newtonian viscous fluid models with learned rheology accurately reproduce Lagrangian sea ice simulations

  ArXiv.org · 2025-09-19

  preprintOpen accessSenior author

  Polar sea ice is crucial to Earth's climate system. Its dynamics also affect coastal communities, wildlife, and global shipping. Sea ice is typically modeled as a continuum fluid using a model proposed almost 50 years ago, which is moderately accurate for packed ice, but loses its predictive accuracy outside of the central ice pack. Discrete element methods (DEMs), which are commonly used for modeling granular media, offer an alternative by resolving the behavior of individual ice floes, including collisions, frictional contact, fracture, and ridging. However, DEMs are generally too costly for large-scale simulations. To address this, we present a framework for inferring rheological behavior from DEM velocity data. We characterize isotropic constitutive laws as scalar functions of the principal invariants of the strain-rate tensor. These functions are parameterized by neural networks trained on DEM data. By combining machine learning and finite element methods, we incorporate the governing partial differential equation (PDE) into the training, requiring to solve a PDE-constrained optimization problem for the network parameters. We focus on unidirectional parallel shear flows, which allow us to infer the effective shear viscosity. We find that, over a wide range of ice concentrations, the velocity fields observed in a complex sea ice DEM can be captured by a nonlinear rheology. Depending on the ice concentration, a shear-thinning or a shear-thickening behavior is observed. Moreover, the effective shear viscosity is found to increase by several orders of magnitude with changes as small as 5% in the sea ice concentration. We show that the learned rheology generalizes to different forcing scenarios, time-dependent problems, and settings in which compressibility is not a dominant factor.

  PublisherOA PDFDOI

• Modelling sea ice in the marginal ice zone as a dense granular flow with rheology inferred from discrete element model data

  Journal of Fluid Mechanics · 2024-11-25 · 7 citations

  articleOpen accessSenior author

  The marginal ice zone represents the periphery of the sea ice cover. In this region, the macroscale behaviour of the sea ice results from collisions and enduring contact between ice floes. This configuration closely resembles that of dense granular flows, which have been modelled successfully with the $\mu (I)$ rheology. Here, we present a continuum model based on the $\mu (I)$ rheology that treats sea ice as a compressible fluid, with the local sea ice concentration given by a dilatancy function $\varPhi (I)$ . We infer expressions for $\mu (I)$ and $\varPhi (I)$ by nonlinear regression using data produced with a discrete element method (DEM) that considers polygon-shaped ice floes. We do this by driving the sea ice with a one-dimensional shearing ocean current. The resulting continuum model is a nonlinear system of equations with the sea ice velocity, local concentration and pressure as unknowns. The rheology is given by the sum of a plastic term and a viscous term. In the context of a periodic patch of ocean, which is effectively a one-dimensional problem, and under steady conditions, we prove this system to be well-posed, present a numerical algorithm for solving it, and compare its solutions to those of the DEM. These comparisons demonstrate the continuum model's ability to capture most of the DEM results accurately. The continuum model is particularly accurate for ocean currents faster than 0.25 m s $^{-1}$ ; however, for low concentrations and slow ocean currents, the continuum model is less effective in capturing the DEM results. In the latter case, the lack of accuracy of the continuum model is found to be accompanied by the breakdown of a balance between the average shear stress and the integrated ocean drag extracted from the DEM. Since this balance is expected to hold independently of our choice of rheology, this finding indicates that continuum models might not be able to describe sea ice dynamics for low concentrations and slow ocean currents.

  PublisherOA PDFDOI

Recent grants

• Collaborative Research: Forward and inverse models of global plate motions and plate interactions

  NSF · $98k · 2017–2019

• Classification of Methods for Bayesian Inverse Problems Governed by Partial Differential Equations

  NSF · $180k · 2017–2021

• CDS&E: Collaborative Research: A Bayesian inference/prediction/control framework for optimal management of CO2 sequestration

  NSF · $140k · 2015–2017

Frequent coauthors

• Omar Ghattas

  The University of Texas at Austin

  68 shared

• Michael Gurnis

  California Institute of Technology

  41 shared

• Noémi Petra

  University of California, Merced

  38 shared

• Florian Wechsung

  31 shared

• Carsten Burstedde

  University of Bonn

  28 shared

• Antoine Cerfon

  New York University

  28 shared

• Andrew Giuliani

  Flatiron Institute

  28 shared

• Johann Rudi

  24 shared

Labs

• Georg Stadler's LabPI

  Research in applied and computational mathematics, Bayesian inverse problems, extreme events, scientific ML, optimization with PDEs, and parallel scientific computing.